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I thought it was very interesting that the Nesivos Shalom chose to take this as referring only and specifically to korbanot and not to any other mitzvah. The reason the korbanot are invalidated due to intent is because the entire purpose of the korban is to atone for one's sin, and to feel as though what is being done to the korban is what ought to be done to you. Other mitzvot, however, still have value even if someone performs them for the sake of another person's good opinion, or to earn money, or some such motive. This made me think of Tsemakh Atlas, who upbraids people for their lack of pure motives, taking an approach quite opposite that of the Nesivos Shalom. I am currently rereading The Yeshiva (one of the greatest Jewish books ever written). Here are the relevant excerpts from the book.
Into the store came Reb Kopel Kaufman, a community volunteer. He wore a long gaberdine, shiny with stains from grease, Kiddush wine, and wax from the Havdola candles. Reb Kopel was always busy and bustling about, collecting donations for the Talmud Torah and for the orphanage. Everyone in Lomzhe knew that he didn't take a penny for himself- he was supported by his wife's little store. Tsemakh too had become acquainted with him and didn't like Reb Kopel's lusty groaning while telling about the needy little Talmud children. This time Reb Kopel came in with a mouthful of sighs to collect his monthly donation for the orphanage. He took his notebook out of his pocket, licked his blue pencil, and waited for the Stupels' brother-in-law to tell him how much to write down. Tsemakh gave him a contribution and declined the receipt.
"As far as the money is concerned, I trust you. But I don't trust your goodness. It makes me sad to see people who are so compassionate they literally take delight in their compassion. For a lustful man even compassion is a lust, and you actually sweat with pleasure when you weep over these orphans."
Reb Kopel stood there open-mouthed, his tongue smeared with the blue of his pencil.
"Is...is that the way you talk to me?" he stammered and began to sob. "A man who is a faithful servant of the community? I run around day and night collecting charity and eating my heart out before I get a donation."
Tsemakh gave him a searing glance and said furiously, "That's exactly what I mean. When a man helps someone, he should talk as little as possible about it, and not make a big noise or bustle about the needy person as if he were a corpse with no kin. But you, who are supposedly a faithful servant of the community, you make a big noise about your compassion and brag about your kindness. That proves you're motivated by your own pleasure and honor, and not the orphans' welfare."
Reb Kopel Kaufman sidled out of the store as if afraid that wet towels might be thrown after him. Volodya was beaming.
"Wonderful, Tsemakh! You really gave it to him. That's the way to talk to these community busybodies, these public-spirited do-gooders!" the hefty Volodya screeched with joy in a thin, eunuchlike voice. He never refused to make a contribution, but he despised these community workers and also ridiculed his brother Naum: "That showoff has run out again in his frock coat and top hat for some bigwig's reception."
In the afternoon Reb Enzele came into the store. He was a small man with a tiny nose and a tidy white little beard. From his neat and pious demeanor it was apparent that his thoughts were clean and his lips spoke no evil. Even Reb Enzele's occupation was connected with Sabbath holiness. A bronzesmith, he silvered candelabra and gilded the Torah's crowns and little beds. Each time he entered and left a Jewish house he tiptoed to kiss the mezuza on the doorpost. He permitted his tefillin to be examined only by the man with the longest beard in town, and for Sukkos he bought the finest esrog. Now he had entered the Stupels' store to pay for his Passover matzo flour. His kind eyes beamed with joy and trust. Reb Enzele said good morning to everyone and had laready taken out his purse.
At the same time a woman entered the store to buy flour for her Sabbath challas. Her face was despondent; she sighed aloud and poured out her heart to Volodya. "I really don't know how I can bring myself to bake and cook. Not even a month has passed since the Nareva River took my sister's one and only child. Oh, Lord, how many doctors and Hassidic rebbes my sister and brother-in-law went to see before they finally had a baby! How the parents tended and fussed over their little boy until he grew up! Then one Sabbath Itzikl never returned. The Nareva had taken him."
Even though Volodya was hearing this story for the twentieth time, he wrinkled his brows and had to strain not to shed a tear. He empathized with the anguish of the parents. Moreover, he was almost choked with gloom that there was no little blond girl in white socks running around in his home.
"What a tragedy! May it befall no other Jews! What a tragedy!" Reb Enzele the bronzesmith sadly shook his head. "But God is just and his ways are just. When a Jewish child goes swimming on the Sabbath..."
He had scarcely ended the sentence when Tsemakh turned a pair of blazing eyes on him and let fly a torrent of words. "Job's friends were much holier than you, but still God was furious with them for their remarking that Job had probably sinned and deserved his troubles. When a man feels that the world has crumbled beneath him, it's cruel to console him by saying he will overcome his misfortune. It's even more cruel to justify the heavenly decree- for someone else. And besides being cruel, it's also toadying and hypocritical. One toadies up to God that he is just and his ways are just- for the next fellow- to save oneself from the very same judgement. But God in heaven sees through such phony little plaster saints."
The bronzesmith ran out of the store as though his gaberdine had been set on fire by Tsemakh's blazing eyes. The clerks followed to apologize, but Reb Enzele waved his hands- he didn't want to hear a word. He quickly paid them for the Passover flour and fled through the market. Everyone saw the old man shaking his head from side to side. "No, no, I've never been so insulted in my life, and for no reason."
~The Yeshiva by Chaim Grade, Volume 1, 62-64
Slava, depressed, said nothing. In their first private conversation, she hadn't taken him seriously when he told her that a Musarnik couldn't enjoy life; now she saw that he was right. The fire in Tsemakh also gradually subsided, and both sat gloomily silent, like a poor couple at a bare table the morning after a holiday.
"You won't be able to make the world over, but you'll ruin our happiness. Ever since time began, people have been both wild beasts and angels," Slava murmured sadly.
"That's just the point," Tsemakh answered. "All my life I've learned that when someone flutters with the wings of an angel, one must look beneath his wings to see if the body of a beast isn't lurking there in a sweaty and hairy hide."
~The Yeshiva by Chaim Grade, Volume 1, page 74